The aims of this paper are: (1) to present a similarity generating function composed of elevation, scatter and shape parameters; (2) to describe linear models for integrating these parameters either for euclidean distance or vector-product association indices; and (3) to suggest a computational strategy based upon the Eckart-Young (1936) theorem that has certain advantages for minimizing the effects of measurement error in estimating profile similarity. Given these developments, the investigator may differentiate the independent contribution of each parameter to more global indices of resemblance. A brief example from the classification of psychopathology is discussed.
Get full access to this article
View all access options for this article.
References
1.
Cattell, R. B.r and other coefficients of pattern similarity. Psychometrika, 1949, 14, 279-298.
2.
Cohen, J.rc: A profile similarity coefficient invariant over variable reflection, Psychological Bulletin , 1969, 71, 281-284.
3.
Cronbach, L. J. and Gleser, G.Assessing similarity between profiles. Psychological Bulletin, 1953, 6, 456-473.
4.
Eckart, C. and Young, G.The appoximation of one matrix by another of lower rank . Psychometrika, 1936, 1, 211-218.
5.
Fleiss, J. L. and Zubin, J.On the methods and theory of clustering. Multivariate Behavioral Research, 1969, 4, 235-250.
6.
Gleason, T. C. and Staelin, R.Improving the metric quality of questionnaire data. Psychometrika, 1973, 38, 393-410.
7.
Gollob, H. F.Confounding of sources of variation in factor-analytic techniques. Psychological Bulletin, 1968, 70, 330-344.
8.
Guertin, W. H.The search for recurring patterns among individual profiles. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 1966, 26, 151-165.
9.
Horn, J. L.Factor analysis with variables of different metric. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT , 1969, 29, 753-762.
10.
Horst, P.Factor analysis of data matrices . New York: Holt, Rinehart & Winston, 1965.
11.
Lanyon, R. I.A handbook of MMPI group profiles . Minneapolis: University of Minnesota Press, 1968.
12.
Lorr, M.Explorations in typing psychotics . Oxford: Pergamon Press, 1966.
13.
Morrison, D. F.Multivariate statistical methods . New York: McGraw-Hill, 1967.
14.
Nunnally, J. C.The analysis of profile data . Psychological Bulletin, 1962, 59, 311-319.
15.
Overall, J. E. and Klett, C. J.Applied multivariate analysis. New York: McGraw-Hill, 1972.
16.
Penrose, L. S.Distance, size and shape. Annals of Eugenics, 1954, 18, 337-343.
17.
Skinner, H. A.The eyes that fix you: A model for classification research. Canadian Psychological Review , 1977, 18, 142-151.
18.
Sneath, P.H.A. and Sokal, R. R.Numerical taxonomy. San Francisco : Freeman, 1973.
19.
Stewart, G. W.Introduction to matrix computations . New York: Academic Press, 1973.
20.
Wishart, D.A general tripartite clustering method and similarity generating function. Report No. R-31, Statistics 1 Division, Civil Service Department, Whitehall, London, England, April, 1972.
